On the C1-equivalence of essentially nonlinear systems of differential equations near an asymptotically stable equilibrium point

Research output: Contribution to journalArticleResearchpeer-review

Abstract

A system of differential equations is considered for which the origin is an asymptotically stable equilibrium point and the Taylor expansion in a neighborhood of this point has no linear terms. Under the assumption that the logarithmic norm of the Jacobian matrix is negative definite, it is proved that this system is locally C1 equivalent to any of its perturbations of sufficiently high order of vanishing.

Original languageEnglish
Pages (from-to)9-17
Number of pages9
JournalVestnik St. Petersburg University: Mathematics
Volume48
Issue number1
DOIs
StatePublished - 1 Jan 2015

Keywords

  • essentially nonlinear system
  • logarithmic norm
  • smooth conjugacy
  • smooth equivalence

Scopus subject areas

  • Mathematics(all)

Cite this

@article{77fb49f1818c4280a389ae954726e037,
title = "On the C1-equivalence of essentially nonlinear systems of differential equations near an asymptotically stable equilibrium point",
abstract = "A system of differential equations is considered for which the origin is an asymptotically stable equilibrium point and the Taylor expansion in a neighborhood of this point has no linear terms. Under the assumption that the logarithmic norm of the Jacobian matrix is negative definite, it is proved that this system is locally C1 equivalent to any of its perturbations of sufficiently high order of vanishing.",
keywords = "essentially nonlinear system, logarithmic norm, smooth conjugacy, smooth equivalence",
author = "Iljin, {Yu A.}",
note = "Vestnik St. Petersburg University: Mathematics. 2015. Volume 48, issue 1, pp.9-17.",
year = "2015",
month = "1",
day = "1",
doi = "10.3103/S1063454115010057",
language = "English",
volume = "48",
pages = "9--17",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "1",

}

On the C1-equivalence of essentially nonlinear systems of differential equations near an asymptotically stable equilibrium point. / Iljin, Yu A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 48, No. 1, 01.01.2015, p. 9-17.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - On the C1-equivalence of essentially nonlinear systems of differential equations near an asymptotically stable equilibrium point

AU - Iljin, Yu A.

N1 - Vestnik St. Petersburg University: Mathematics. 2015. Volume 48, issue 1, pp.9-17.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - A system of differential equations is considered for which the origin is an asymptotically stable equilibrium point and the Taylor expansion in a neighborhood of this point has no linear terms. Under the assumption that the logarithmic norm of the Jacobian matrix is negative definite, it is proved that this system is locally C1 equivalent to any of its perturbations of sufficiently high order of vanishing.

AB - A system of differential equations is considered for which the origin is an asymptotically stable equilibrium point and the Taylor expansion in a neighborhood of this point has no linear terms. Under the assumption that the logarithmic norm of the Jacobian matrix is negative definite, it is proved that this system is locally C1 equivalent to any of its perturbations of sufficiently high order of vanishing.

KW - essentially nonlinear system

KW - logarithmic norm

KW - smooth conjugacy

KW - smooth equivalence

UR - http://www.scopus.com/inward/record.url?scp=84925308266&partnerID=8YFLogxK

U2 - 10.3103/S1063454115010057

DO - 10.3103/S1063454115010057

M3 - Article

VL - 48

SP - 9

EP - 17

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -